Problem: Rewrite as a simplified fraction. ${0.69\overline{7} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 697.7777...\\ 100x &= 69.7777...\end{align*}}$ Subtracting the two equations, we have: ${900x = 628}$ ${x = \dfrac{628}{900}} $ ${x = \dfrac{157}{225}} $